The paper discusses the principle of power amplification, as it can be found in many systems powered by PV panels and buffered by batteries. Under different categories of application examples one is given by compacting containers for plastic or other waste materials. The main goal of such systems is to supply high-power intermittent systems from low power sources. The studied example discusses an energy harvesting system using a low power solar PV collection system that is dedicated to power a specific application, sequentially operated at high power. The transformation of the power level is achieved using intermediary storage, where the charging sequence is characterized by a very low power level for longer time, followed by a shorter discharge sequence of the storage means with a much higher instantaneous power. The performance of the PV harvesting system is discussed from the point of view of its energy efficiency. Several solutions are discussed, and finally, a new 2-stage harvesting system is introduced. The requirement of a multistage amplification system is related to the power amplification ratio itself. The design method for the system relies on the concept of the so-called “Modified Ragone Representation”, MRR, that is shortly introduced in the paper. A prototype realization of the two-stage system is also presented.
Energy storage devices or accumulators are often inserted to enable a system to cope with extremes of demand using a less powerful source, to respond more quickly to a temporary demand, or to smooth out pulsations. More recently, new applications of solar powered devices are appearing, allowing many tasks that need short-term high-power demand, while being powered by small photovoltaic cells. Collecting solar power with PV panels with a relatively high efficiency is enabled by following strict conditions related to the maximum solar irradiation and to the conversion efficiency of the PV cells. Usually, PV installations have the property of consuming a large surface for a defined power level in the order of magnitude of 10 m2 for 1 kWp. Specific applications such as compacting waste collectors or other applications as the composter machine are characterized by the small surface of their PV collectors and through the higher instantaneous power needed by the internal actuator. Because of the typical intermittency of solar irradiation, but also in order to provide a given level of power to the final application, this kind of systems usually need embed energy storage components such as batteries. High power density is generally required in order to achieve good energy efficiency.
One can assume that usually, the power density of an accumulator during the charge process is identical to its discharge power density. In the presented application framework, the real operation conditions are different. Indeed, even if the averaged power required is relatively low, the impulse power peak can be several orders of magnitude higher than the latter. In such a case, an energy harvesting system with very low input power level can be designed. This paper will introduce the design criteria of such harvesting systems that are able to provide a high power level to the final application, with the help of an energy storage element. During the discharge of that accumulator, a high power density must be available in order to keep the energy efficiency at a good level.
The principle of Power Amplification
A given amount of energy can be represented by the time integral of an instantaneous value of power, leading to the representation by a geometric surface. The simplified model of figure 2 represents the corresponding energy amount under the curve of a given power level. In this representation, the power P1 is kept constant during the time duration t1. At the right side of the figure, the higher power level P2 is also kept constant during the shorter time duration t2.
In the idealized case where the energy amount would be kept constant in the transformation from P1*t1 to P2*t2, the energy efficiency is defined as unity. The power amplification factor PAF is defined as the ratio of P2/P1. In the non-ideal case, the energy efficiency is defined as P2*t2 / P1*t1
For both the charge and discharge process of an energy storage device, the energy efficiency can be calculated. Its dependency from the actual value of the exchange power level has been highlighted in  and .
2.1 The Modified Ragone Representation MRR
Figure 3 is one general representation that illustrates the energy losses of one storage device, where both effects of first the self-discharge loss and second the load-related loss caused by the internal series resistor of an ideal battery are represented. Figure 3a shows the equivalent scheme of an ideal battery, where an ideal voltage source (U0) is represented, together with the parallel resistor Rp and the series resistor Rs. The amount of stored energy is represented through the quantity W0.
Figure 3b shows the so called Modified Ragone Representation MRR , indicating the amount of energy to be extracted from a storage device while being discharged from a full state of charge down to zero. The red curve illustrates the properties of an energy-type accumulator, the blue curve is related to a power-type accumulator.
The diagram represents the energy amount that one can recover from an ideal storage device taking into account the self-discharge (Rp in Figure 3a), and also the internal loss in the series resistor Rs. The horizontal scale of Fig. 3b represents the power at what the energy is recovered. The scale is chosen as a logarithmic scale in order to represent as well the extreme low power values, as the high solicitations. The left side of these diagrams illustrate the domain where the power level for the discharge is in the range of the self-discharge power. The extracted energy amount is near zero. On the right side of the diagrams, the operation conditions are that the internal losses due to the presence of the series resistor are strongly reducing the amount of extractable energy.
In the middle of the curves, the normal operation domain is represented where an acceptable amount of energy can be extracted over about 2 or 3 decades of the power range.
For the charging process, similar curves can be defined, because the self-discharge as well as the internal series losses are modelled through the same equivalent scheme.
As a consequence, one can recommend to charge and discharge a storage device at a power level situated between the positive and negative slope of the MRR curve, preferably at power levels where the curve reaches sufficient high values.
Energy harvesting with small photovoltaic panels and a two stage amplification
An energy harvesting system is developed with the goal to provide energy to a specific application characterized by an intermittent operation. The harvesting of the energy amount is done from a minimal surface of PV panels. A cascaded energy conversion and storage system overtakes the function of the power transformation.
The efficiency of the 1st stage power amplification with supercapacitors
As explained at the beginning of this paper, the first stage of the power amplification is achieved using direct coupled supercapacitors. Figure 6 highlights the operation principle of the so called « riding cap » , where the power delivered by the PV panels PPV is drawn on the left side of the figure as a function of the panels voltage VPV. The corresponding value of the voltage of the PV panels that is identical to the voltage of the direct connected supercapacitors is represented as a time-function in the upper right part of the figure.
The instantaneous power, fed to and delivered by the supercapacitors is represented in the lower curve of figure 6. Pin is the value of the charging power level of the supercapacitors, and Pout is their discharging value. The charging and discharging durations are indicated as tin and tout. In the following calculation of the energy efficiency of this first power amplification stage, the variation of the value of the supercapacitor’s voltge is neglected, due to the fact that the hysteresis of the sliding-mode controller is kept small. The calculation is done with a constant parameter USC corresponding to the mean value.
The calculation of the energy efficiency of the power amplification is based on an equivalent scheme . A simplified calculation is given here, where not only the voltage variations of the supercapacitors is neglected, but where the charging/discharging current is kept constant. A more accurate calculation of this efficiency can be found in .
The Modified Ragone Representation (MRR) for the evaluation of the efficiency of a two stage amplification system
The method of the Modified Ragone Representation has been presented in section 2.1 for a one-stage storage system. The two stage system represented in figure 4 can be analyzed through the same tool of the Modified Ragone Representation. The properties of the studdied system represented in figure 1b), eg. an input PV power of around 70 W and an application power level of 5kW, result to a minimal value of the global power amplification factor PAFtot= 70. But in reality, when the sun radiation is poor, this factor can be much higher, and reach values of several hundreds. This was the main motivation of the realization of the two-stage system. The individual energetic properties of the components of the two stage system are represented in the diagram of figure 9. First the blue lines of the PV panels are drawn (one line per solar irradiance value), where the power should ideally be kept at the MPPT point corresponding to the unity value. The intersections with the black line of the Modified Ragone Representation of the supercapacitors show that the choice of these component is well adapted, and the MRR of the supercapacitors gives the value of the energy efficiency of this first energy transfer. The power level of the PV generator (P1 in figure 3) due to sunshine variations is represented as a variable power through the different blue curves in figure 9, it is comprized between 10 and 70 W. Then the energy transfer from the supercapacitors to the hydraulic accumulator is influenced as well by the MRR of the former component (the supercapacitors) for its discharge, as by the MRR of the hydraulic accumulator itself during its own charging. This energy transfer is represented through the green zone of figure 9, where one can see the optimal design due to simultaneous intersection of the curves at their respective maximums. The width of the green zone in figure 9 corresponds to the power variation of the charging impulses of the hydraulic accumulator due to the variation of its internal pressure related to its state of charge. Finally, the high power value of the final application (5kW) is represented by the vertical dotted red line. It can be read that the intersection with the MRR of the hydraulic accumulator corresponds to an acceptable energy exchange, the intersection point beeing in the region of the high performance of the bladder. One can easily see also that there is a total incompatibility between the curves of the PV panel and the final application, and also an incompatibility between the supercapacitive pre-storage and the same final application. The total power amplification factor of this two-stage application beeing equal to 5kW / 70W = 70 in the case of the highest PV power collected.
Figure 10 illustrates the experimental verification equipment realized within the system-study and development. The system has been connected to a 100 Wp PV panel, and the output of the hydraulic accumulator has been connected to one hydraulic motor, itself coupled to a DC generator (according Fig. 3). The figure illustrates mainly the accumulation devices such as the supercapacitors (1) and the hydraulic accumulator (3), as well as motor-pump and control electronics.
The operation of the realized system is illustrated through the curves of figure 11. The successive rise and decrease of the pressure in the bladder illustrates the total cycle of the application (around 350s). The record includes also the value of the supercapacitor’s voltage Uscap, and the current Ipv provided by the PV panels. Within one total cycle of the charge and discharge of the second stage (the hydraulic accumulator), there are six “sub-cycles” of charge and discharge of the supercapacitors.
The slopes of the charge and discharge of the supercapacitors in figure 11 are of the same order of magnitude, illustrating the operation at high insolation of the PV panels. For an operation with low sun, the charging slope will be lowered. According the MRR of figure 9, a too low sunshine could lead to a poor efficiency if the intersections of the PV characteristics are situated at the left slope of the MMR diagram of the supercapacitors.
A two-stage power amplification equipment has been developed as an energy harvesting system for powering an application where the needed power level for the final application is not compatible with the available power of the small dimension PV collector. The first stage of the power amplification system has been realized with a bank of supercapcitors, particularly suited for the pre-storage of the low power delivered by the PV panels. The second stage is using a hydraulic accumulator, which can easily provide the high output power of the final application. The design of the equipment providing a power amplification factor higher than 70 has been done using the method of the MRR (Modified Ragone Representation), showing the good matching of the system components from the point of view of the partial and global energy efficiency. The input power levels of the global system are in the range of 10-70 W from the PV generator, while up to 5 kW are drawn from the final application.